Abstract
Via studying the relation between isosceles orthogonality and the lengths of segments contained in the unit sphere, existing results on the uniqueness of isosceles orthogonality are improved.
Similar content being viewed by others
References
Alonso J.: Uniqueness properties of isosceles orthogonality in normed linear spaces. Ann. Sci. Math. Quebec 18, 25–38 (1994)
Alonso J., Benítez C.: Orthogonality in normed linear spaces: a survey part I: main properties. Extracta Math. 3, 1–15 (1988)
Alonso J., Benítez C.: Orthogonality in normed linear spaces: a survey part II: relations between main orthogonalities. Extracta Math. 4, 121–131 (1989)
Birkhoff G.: Orthogonality in linear metric spaces. Duke Math. J. 1, 169–172 (1935)
James R.C.: Orthogonality in normed linear spaces. Duke Math. J. 12, 291–301 (1945)
Kapoor O.P., Prasad J.: Orthogonality and characterizations of inner product spaces. Bull. Aust. Math. Soc. 19, 403–416 (1978)
Klein, R.: Concrete and abstract Voronoi diagrams, Lecture Notes in Computer Science 400. Springer, Berlin (1989)
Martini H., Swanepoel K.J.: The geometry of Minkowski spaces—a survey. Part II. Expo. Math. 22, 93–144 (2004)
Martini H., Swanepoel K.J.: Antinorms and Radon curves. Aequationes Math. 72, 110–138 (2006)
Martini H., Swanepoel K.J., Weiß G.: The geometry of Minkowski spaces—a survey. Part I. Expo. Math. 19, 97–142 (2001)
Martini H., Swanepoel K.J., Weiß G.: The Fermat-Torricelli problem in normed planes and spaces. J. Optim. Theory Appl. 115, 283–314 (2002)
Martini H., Wu S.: Radial projections of bisectors in Minkowski spaces. Extracta Math. 23, 7–28 (2008)
Martini H., Wu S.: On maps preserving isosceles orthogonality in normed linear spaces. Note Mat. 29, 55–59 (2009)
Roberts B.D.: On the geometry of abstract vector spaces. Tôhoku Math. J. 39, 42–59 (1934)
Singer I.: Angeles abstraits et fonctions trigonométriques dans les espaces de Banach. Acad. R. P. Romîne. Bull. Şti. Secţ. Şti. Mat. Fiz. 9, 29–42 (1957)
Thompson A.C.: Minkowski Geometry, Encyclopedia of Mathematics and its Applications, vol. 63. Cambridge University Press, Cambridge (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
The research of the first and third named authors is supported by National Natural Science Foundation of China (grant number 11001068). The third named author is also supported by a grant from Harbin University of Science and Technology (grant number 2009YF028).
Rights and permissions
About this article
Cite this article
Ji, D., Li, J. & Wu, S. On the Uniqueness of Isosceles Orthogonality in Normed Linear Spaces. Results. Math. 59, 157–162 (2011). https://doi.org/10.1007/s00025-010-0069-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-010-0069-6